Abstract
It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics.
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Torza, A. How to Lewis a Kripke–Hintikka. Synthese 190, 743–779 (2013). https://doi.org/10.1007/s11229-012-0201-0
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DOI: https://doi.org/10.1007/s11229-012-0201-0